Abstract: A clear understanding of freezing and melting is of great importance in many applications starting from growth of nano-crystals in solutions for solar cells to making the perfect ice cream. This work aims to understand how the flow of the liquid phase affects the freezing process (solid-liquid phase transition).This talk will outline the problem with the perspective of an interdisciplinary mathematician.The mathematical challenges involved in developing a solvable predictive model and developing efficient methods of solving the so developed model will be discussed.Some results demonstrating the predictive ability of the so developed approach will be discussed.

This work was done in collaboration with John Lowengrub and Aparna Baskaran

Abstract:In the next few years a new generation of gravitational wave detectors will allow us to "listen" some of the most energetic events in the universe; the coalescence of binary compact objects such as black holes and/or neutron stars. If the magnetic field around these objects is sufficiently strong, the binary may produce an electromagnetic burst which we may be able to "see", especially if it is in the form of a collimated jet. A new era of multi-messenger astronomy, involving detections of EM, GW and possible neutrino signals, will provide more insight into the physical processes involved in the collisions. After giving an overview on gravitational waves and the underlying equations, I will describe the dynamics of compact binary mergers, focusing on the gravitational waveforms and the possible EM counterparts from these systems.

Date, Location:

2013-04-23

Dr. Casian Pantea 4/22/2013

Abstract: The behavior of biological interaction networks (such as networks of biochemical reactions, infectious diseases within a population, or species in an ecosystem) is commonly modeled using intricate systems of differential equations. These models usually contain a large number of parameters whose values are rarely known in practice. However, even when no information regarding parameter values is available, wide classes of interaction networks can be shown to have surprisingly stable behavior, induced by the topology of the network alone. In this talk I will consider some of the problems and results of chemical reaction network theory, a body of work which attacks the question: "What behaviours of an interaction network are a function of its structure, and are robust to different choices of parameters?" In particular, I will discuss recent results relating the topology of a network with the possibility for Hopf bifurcations in the corresponding ODE system.

Date, Location:

2013-04-22

Professor Yue Zhao 4/19/2013

On Edge Chromatic
Critical Graphs

Date: 4/19/2013
Time: 3:30PM-4:30PM,
Place: 315 Armstrong Hall

Professor Yue Zhao

Abstract: Around 1965, Vizing proposed four conjectures about edge
chromatic critical graphs. Since then, many people have been working on
these conjectures. But these four conjectures remain open. In this talk, we will present some results on these four conjectures.

Abstract: Even though binary black hole (BBH) systems are expected to come in a wide range of masses, only the mergers of supermassive black holes at the centers of galaxies are expected to live in gas-rich environments. The presence of matter opens up the possibility that gravitational aspects of the binary's interaction can be transmitted electromagnetically to distant observers via dissipation of gas motion. Matching theoretical predictions to observations of systems before and after merger has the potential to improve our estimates of merger rates, and tell us about the spin and mass distributions of supermassive black holes. Seeing the light from the precise moment of merger---if such a robust signature exists---presents us with additional information such as more evidence that black holes merge, how material behaves in the strong-field dynamical regime of gravity, and a new and independent class of redshift-distance measurements if found with accompanying gravitational radiation. All of these exciting possibilities require realistic predictions for how magnetized gas responds to a BBH evolution. Therefore, realistic, accurate magnetohydrodynamics simulations using Einstein's theory of General Relativity must be performed. Such calculations require the numerical solution of the partial differential equations that describe the gravity and matter dynamics. The accuracy of the solution demands using state-of-the-art computational techniques and massive supercomputing resources. In this talk, I will survey what we know about accreting single black hole systems, to gain an understanding of what we may expect through a simpler, better known problem. Then, I will provide a theoretical introduction to the topic and highlight key aspect of the numerical methods we employ. The results from our first steps on this new campaign will be presented, including the prediction of a nontrivial electromagnetic period signal from an orbiting binary black hole. We will show how this periodic signal could be used to determine properties of the orbit. I will then conclude with a few ideas we have for future work on this endeavor.

Dr. Noble is currently an Associate Research Scientist at the Center for Computational Relativity and Gravitation (CCRG) at the Rochester Institute of Technology and is a candidate for a position in the Department of Mathematics.

Professor Bradley Lucier 4/4/2013

A few years ago the chemist Dor Ben-Amotz at Purdue University approached
me with the story of a new type of Raman spectrometer he was building.
Conceptually, a spectrometer counts photons. The range of possible
frequencies of the photons is divided into a number of bins. Typical
spectrometers count photons in all frequency bins separately and in
parallel, but somewhat inaccurately. The new spectrometer would, in each
measurement, collect together photons from an arbitrary set of frequency
bins, and count very accurately the aggregate number of photons that hit
those bins. Ben-Amotz calls the latter measurement technique "compressive
detection".

The questions were: How to use the new machine effectively, or, better yet,
optimally? And, for some purposes, would the new spectrometer outperform
"typical" spectrometers.

The mathematical answers come from an area of statistics called,
appropriately enough, Optimal Design of Experiments. Understanding the
problem formulation requires only an undergraduate knowledge of statistics
(mean, variance, and Poisson random variables). Solving the problem seems
to require new mathematical techniques.

In practice the new approach works well, allowing classification of samples
of certain pairs of chemicals in as little as 30 microseconds, while
counting as few as a dozen photons. We have applied the technique to
chemical "imaging", where we can classify the powder at each location on a
slide as either glucose or fructose, say, in as little as 100 microseconds,
counting about 30 photons, per image pixel.

This is joint work with Dor Ben-Amotz and his post-docs and graduate
students (especially David Wilcox) and Greg Buzzard in mathematics at
Purdue.

Date, Location:

2013-04-04

Professor Dehua Wang 3/21/2013

Mixed-type problems for transonic
flows and isometric embeddings

Professor Dehua Wang

Date: 3/21/2013
Time: 2:30-3:30 PM
Place: 312 Clark Hall

Abstract:Some mixed-type problems of transonic flows in gas dynamics and isometric embeddings in geometry will be discussed. Connections between the two problems, and global existence of weak solutions will be presented.

Date, Location:

2013-03-21

Professor Ju Zhou 3/18/2013

Pancyclicity of 4-connected $\{K_{1,3},Z_8\}$-free graphs

Professor Ju Zhou

Date: 3/18/2013
Time: 3:30-4:30 PM
Place: 315 Armstrong Hall

Abstract: A graph $G$ is said to be pancyclic if $G$ contains cycles of
lengths from 3 to $|V(G)|$. Ron Gould in 2011 raised an open
problem to determine the induced subgraphs that should be
forbidden so that 4-connectedness will assure pancyclicity. In
this paper, we show that every 4-connected claw-free $Z_8$-free
graph is either pancyclic or is the line graph of the Petersen
graph. This implies that every 4-connected claw-free $Z_6$-free
graph is pancyclic, and every 5-connected claw-free $Z_8$-free
graph is pancyclic.